help for algebraic structures 2
Define the set M and the binary operation â—¦ in the following way:
M = x ; x âˆˆ R(real number), x not equal to 1/5 , a â—¦ b = a + b + 5a Â· b
where + and Â· denote the usual addition and multiplication in R. Show that (M, â—¦) is a group. Determine whether this group is Abelian.